Bipartite Entanglement in Continuous-Variable Cluster States

Abstract

We present a study of the entanglement properties of Gaussian cluster states, proposed as a universal resource for continuous-variable quantum computing. A central aim is to compare mathematically-idealized cluster states defined using quadrature eigenstates, which have infinite squeezing and cannot exist in nature, with Gaussian approximations which are experimentally accessible. Adopting widely-used definitions, we first review the key concepts, by analysing a process of teleportation along a continuous-variable quantum wire in the language of matrix product states. Next we consider the bipartite entanglement properties of the wire, providing analytic results. We proceed to grid cluster states, which are universal for the qubit case. To extend our analysis of the bipartite entanglement, we adopt the entropic-entanglement width, a specialized entanglement measure introduced recently by Van den Nest M et al., Phys. Rev. Lett. 97 150504 (2006), adapting their definition to the continuous-variable context. Finally we add the effects of photonic loss, extending our arguments to mixed states. Cumulatively our results point to key differences in the properties of idealized and Gaussian cluster states. Even modest loss rates are found to strongly limit the amount of entanglement. We discuss the implications for the potential of continuous-variable analogues of measurement-based quantum computation.

22 pages

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Cited by in corpus (11)

• Gaussian Quantum Information
• Graphical calculus for Gaussian pure states
• Demonstration of unconditional one-way quantum computations for continuous variables
• Temporal-mode continuous-variable cluster states using linear optics
• Continuous variable quantum computation with spatial degrees of freedom of photons
• Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation
• Compact Gaussian quantum computation by multi-pixel homodyne detection
• Noise analysis of single-qumode Gaussian operations using continuous-variable cluster states
• Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states
• Flexible quantum circuits using scalable continuous-variable cluster states
• Bipartite Entanglement in Continuous-Variable Cluster States